Bayesian FE model updating using nonlinear normal modes: Application to a cantilever beam

This paper investigates the performance of a probabilistic finite element (FE) model updating approach using the Bayesian inference and nonlinear normal mode (NNM) error functions. The considered beam is the European COST Action F3 benchmark and its response in this study is simulated when subjected to a broadband excitation. The simulated response is then contaminated with different levels of Gaussian white noise to represent noisy measurements. The NNMs of the beam are identified from the noisy data by integrating a nonlinear subspace identification method and numerical continuation in a phase separation approach. An initial FE model of the beam is created in Matlab and its parameters are probabilistically updated. The considered updating parameters are the Young’s modulus of the main beam and coefficients of the local geometric nonlinearity. In the proposed FE model updating approach, error functions are defined as the difference between model-predicted and identified NNMs at different energy levels. Posterior probability distributions of the updating parameters are estimated for different levels of measurement noise. The error function is assumed to have a Gaussian distribution. Performance of the updating results are studied for two cases, namely (1) when the error mean is assumed to be zero and the error covariance is known, and (2) when both the error mean and covariance are updated.